

A197432


a(n) = Sum_{k>=0} A030308(n,k)*C(k) where C(k) is the kth Catalan number (A000108).


1



0, 1, 1, 2, 2, 3, 3, 4, 5, 6, 6, 7, 7, 8, 8, 9, 14, 15, 15, 16, 16, 17, 17, 18, 19, 20, 20, 21, 21, 22, 22, 23, 42, 43, 43, 44, 44, 45, 45, 46, 47, 48, 48, 49, 49, 50, 50, 51, 56, 57, 57, 58, 58, 59, 59, 60, 61, 62, 62, 63, 63, 64, 64, 65
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OFFSET

0,4


COMMENTS

Replace 2^k with A000108(k) in binary expansion of n.


LINKS



FORMULA

G.f.: (1/(1  x))*Sum_{k>=0} Catalan number(k)*x^(2^k)/(1 + x^(2^k)).  Ilya Gutkovskiy, Jul 23 2017


EXAMPLE

11 = 1011_2, so a(11) = 1*1 + 1*1 + 0*2 + 1*5 = 7.


CROSSREFS

Other sequences that are built by replacing 2^k in binary representation with other numbers: A022290 (Fibonacci), A029931 (natural numbers), A059590 (factorials), A089625 (primes), A197354 (odd numbers).


KEYWORD

nonn,easy


AUTHOR



STATUS

approved



